Approximate Symmetries of Interplanetary Orbit Determination. the Bepicolombo Case

The Radio science experiment of the BepiColombo mission to the planet Mercury shall allow to solve for the gravity field of the planet up to degree and order 25, for an improved orbit of Mercury and a very accurate verification of Einstein’s theory of gravitation, for measuring the rotation state of the planet, for mapping the topography (in combination with a laser altimeter). To actually obtain all the above results from the range and range-rate data we will have to solve a complex orbit determination problem which is not automatically well posed and numerically stable. The theory of symmetries and rank deficiencies provides the conceptual tools to find the critical steps of the data processing procedure and to overcome the difficulties, providing results adequate for the achievement of the mission science goals. BepiColombo is the next cornerstone mission of planetary exploration of the European Space Agency [Balogh et al. 2000]. It shall launch two spacecraft in orbit around Mercury; one of these , the Mercury Planetary Orbiter (MPO), will investigate mostly the solid planet surface and interior. Information on the interior structure can be obtained only by a geophysical investigation based upon gravimetry, magnetometry and measurement of the planet’s rotation state. Another of the mission goals is to test Einstein’s theory of gravitation by measuring very accurately the orbit of Mercury around the Sun and the propagation of radio waves in the gravity field of the Sun.